What is the Least Common Multiple of 31704 and 31722?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 31704 and 31722 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31704 and 31722, than apply into the LCM equation.

GCF(31704,31722) = 6
LCM(31704,31722) = ( 31704 × 31722) / 6
LCM(31704,31722) = 1005714288 / 6
LCM(31704,31722) = 167619048

Least Common Multiple (LCM) of 31704 and 31722 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31704 and 31722. First we will calculate the prime factors of 31704 and 31722.

Prime Factorization of 31704

Prime Factorization of 31722

Now multiplying the highest exponent prime factors to calculate the LCM of 31704 and 31722.

LCM(31704,31722) = 2³ × 3¹ × 1321¹ × 17¹ × 311¹
LCM(31704,31722) = 167619048